{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In Depth: Decision Trees and Random Forests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously we have looked in depth at a simple generative classifier (naive Bayes; see [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)) and a powerful discriminative classifier (support vector machines; see [In-Depth: Support Vector Machines](05.07-Support-Vector-Machines.ipynb)).\n",
    "Here we'll take a look at another powerful algorithm: a nonparametric algorithm called *random forests*.\n",
    "Random forests are an example of an *ensemble* method, meaning one that relies on aggregating the results of a set of simpler estimators.\n",
    "The somewhat surprising result with such ensemble methods is that the sum can be greater than the parts: that is, the predictive accuracy of a majority vote among a number of estimators can end up being better than that of any of the individual estimators doing the voting!\n",
    "We will see examples of this in the following sections.\n",
    "\n",
    "We begin with the standard imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivating Random Forests: Decision Trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random forests are an example of an ensemble learner built on decision trees.\n",
    "For this reason, we'll start by discussing decision trees themselves.\n",
    "\n",
    "Decision trees are extremely intuitive ways to classify or label objects: you simply ask a series of questions designed to zero in on the classification.\n",
    "For example, if you wanted to build a decision tree to classify animals you come across while on a hike, you might construct the one shown in the following figure."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/05.08-decision-tree.png)\n",
    "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Decision-Tree-Example)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The binary splitting makes this extremely efficient: in a well-constructed tree, each question will cut the number of options by approximately half, very quickly narrowing the options even among a large number of classes.\n",
    "The trick, of course, comes in deciding which questions to ask at each step.\n",
    "In machine learning implementations of decision trees, the questions generally take the form of axis-aligned splits in the data: that is, each node in the tree splits the data into two groups using a cutoff value within one of the features.\n",
    "Let's now look at an example of this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating a Decision Tree\n",
    "\n",
    "Consider the following two-dimensional data, which has one of four class labels (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "X, y = make_blobs(n_samples=300, centers=4,\n",
    "                  random_state=0, cluster_std=1.0)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap='rainbow');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple decision tree built on this data will iteratively split the data along one or the other axis according to some quantitative criterion, and at each level assign the label of the new region according to a majority vote of points within it.\n",
    "The following figure presents a visualization of the first four levels of a decision tree classifier for this data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/05.08-decision-tree-levels.png)\n",
    "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Decision-Tree-Levels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that after the first split, every point in the upper branch remains unchanged, so there is no need to further subdivide this branch.\n",
    "Except for nodes that contain all of one color, at each level *every* region is again split along one of the two features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This process of fitting a decision tree to our data can be done in Scikit-Learn with the ``DecisionTreeClassifier`` estimator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier\n",
    "tree = DecisionTreeClassifier().fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's write a utility function to help us visualize the output of the classifier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def visualize_classifier(model, X, y, ax=None, cmap='rainbow'):\n",
    "    ax = ax or plt.gca()\n",
    "    \n",
    "    # Plot the training points\n",
    "    ax.scatter(X[:, 0], X[:, 1], c=y, s=30, cmap=cmap,\n",
    "               clim=(y.min(), y.max()), zorder=3)\n",
    "    ax.axis('tight')\n",
    "    ax.axis('off')\n",
    "    xlim = ax.get_xlim()\n",
    "    ylim = ax.get_ylim()\n",
    "    \n",
    "    # fit the estimator\n",
    "    model.fit(X, y)\n",
    "    xx, yy = np.meshgrid(np.linspace(*xlim, num=200),\n",
    "                         np.linspace(*ylim, num=200))\n",
    "    Z = model.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)\n",
    "\n",
    "    # Create a color plot with the results\n",
    "    n_classes = len(np.unique(y))\n",
    "    contours = ax.contourf(xx, yy, Z, alpha=0.3,\n",
    "                           levels=np.arange(n_classes + 1) - 0.5,\n",
    "                           cmap=cmap, zorder=1)\n",
    "\n",
    "    ax.set(xlim=xlim, ylim=ylim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can examine what the decision tree classification looks like (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_classifier(DecisionTreeClassifier(), X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you're running this notebook live, you can use the helper script included in the online [appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Helper-Code) to bring up an interactive visualization of the decision tree building process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "27908facf15245bab6735b3bdfa456d6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='depth', index=1, options=(1, 5), value=5), Output()), _dom_classes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# helpers_05_08 is found in the online appendix\n",
    "import helpers_05_08\n",
    "helpers_05_08.plot_tree_interactive(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that as the depth increases, we tend to get very strangely shaped classification regions; for example, at a depth of five, there is a tall and skinny purple region between the yellow and blue regions.\n",
    "It's clear that this is less a result of the true, intrinsic data distribution, and more a result of the particular sampling or noise properties of the data.\n",
    "That is, this decision tree, even at only five levels deep, is clearly overfitting our data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Decision Trees and Overfitting\n",
    "\n",
    "Such overfitting turns out to be a general property of decision trees: it is very easy to go too deep in the tree, and thus to fit details of the particular data rather than the overall properties of the distributions it is drawn from.\n",
    "Another way to see this overfitting is to look at models trained on different subsets of the data—for example, in this figure we train two different trees, each on half of the original data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](images/05.08-decision-tree-overfitting.png)\n",
    "[figure source in Appendix](https://github.com/jakevdp/PythonDataScienceHandbook/blob/master/notebooks/06.00-Figure-Code.ipynb#Decision-Tree-Overfitting)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is clear that in some places the two trees produce consistent results (e.g., in the four corners), while in other places the two trees give very different classifications (e.g., in the regions between any two clusters).\n",
    "The key observation is that the inconsistencies tend to happen where the classification is less certain, and thus by using information from *both* of these trees, we might come up with a better result!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you are running this notebook live, the following function will allow you to interactively display the fits of trees trained on a random subset of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "f280b0c9da354fa395d5313c4f860380",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='random_state', options=(0, 100), value=0), Output()), _dom_classes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# helpers_05_08 is found in the online appendix\n",
    "import helpers_05_08\n",
    "helpers_05_08.randomized_tree_interactive(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just as using information from two trees improves our results, we might expect that using information from many trees would improve our results even further."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ensembles of Estimators: Random Forests\n",
    "\n",
    "This notion—that multiple overfitting estimators can be combined to reduce the effect of this overfitting—is what underlies an ensemble method called *bagging*.\n",
    "Bagging makes use of an ensemble (a grab bag, perhaps) of parallel estimators, each of which overfits the data, and averages the results to find a better classification.\n",
    "An ensemble of randomized decision trees is known as a *random forest*.\n",
    "\n",
    "This type of bagging classification can be done manually using Scikit-Learn's `BaggingClassifier` meta-estimator, as shown here (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "\n",
    "tree = DecisionTreeClassifier()\n",
    "bag = BaggingClassifier(tree, n_estimators=100, max_samples=0.8,\n",
    "                        random_state=1)\n",
    "\n",
    "bag.fit(X, y)\n",
    "visualize_classifier(bag, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we have randomized the data by fitting each estimator with a random subset of 80% of the training points.\n",
    "In practice, decision trees are more effectively randomized by injecting some stochasticity in how the splits are chosen: this way all the data contributes to the fit each time, but the results of the fit still have the desired randomness.\n",
    "For example, when determining which feature to split on, the randomized tree might select from among the top several features.\n",
    "You can read more technical details about these randomization strategies in the [Scikit-Learn documentation](http://scikit-learn.org/stable/modules/ensemble.html#forest) and references within.\n",
    "\n",
    "In Scikit-Learn, such an optimized ensemble of randomized decision trees is implemented in the `RandomForestClassifier` estimator, which takes care of all the randomization automatically.\n",
    "All you need to do is select a number of estimators, and it will very quickly—in parallel, if desired—fit the ensemble of trees (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mqN//dQtc+AFVvztScfRSPPiYCqcUNmb84vejd86t25Xw+vFnw/nvUzuGkSYag9vvUTuE5paRP77HhGZiG93nX1If0ELPTgjl3f77r8pTnMjc9F84773qC6bpKjYZ8Culrj//UnmOPgO+drkKZbh5pMHcFAqAj1+Wn6UXQm35331B722xGPzk13DWO+Edl6rQw4XnwrlvUY+NRNQaPnKJapUt1R8jJXzxW6ry4fNfVyEG01Se8X/ugL/fNGJvkyurX3eP42/YPDrni8aUZ/3siyqss22H2mXd8+DInWPFSjj73fDT38CvroEL3z/+gkgeY8rEDi90dLobBF2HT31YbaMnMjt3qfKwbBa6w7VCgJGbEbanT3nXWaep7ro77lFhiC3bVDJt+jT4widV4grUtvoXP1I1srualYjLZz4KTY3qPLffo6Qv0+nce9eqDHBHB3z9C/CJD8KOXSoG3t1l1984nK074C//BLswHp2Bm26Fy947Qm+WC/stUJUXhYJHc2eNzvnueVC9h30/c+mMSmT2HUM0VKSEr36/+EJy5S9VXH2if549RoSJbXQPPwQsl+mx06dCZcXYr2ewPPV8cYhCSpUcev4leGUVfPj98MHcFIWF+6iSqVLYNvz892rGmQAqKlSSb+5sdd9HL4c164rL6tJpNZ7mkovUzLbCuW3BAFz5bfjsV11OKpWH6/Z3GO7Yn/YOtd4Z09RrkFJddG64RRm7M05Wguctreo1dc+Mu/wTwztvKZpbipONUP4k5oHY1awmoRRiGLD81dIddx57FRPb6E5tgo9dqsqtbEclnjQNfviN8ZvGMBgiYfdGi27Sabj2n3DxO5VHNxB/v1HVoXaXfWXa4Uvfhlv+prbcb2x0r2MGZUzSmdKVBccdpVp3Cw2MlErt7aVX8kfvGEZvqdlQ+NPf4a//Uo0ZpqVqexfuAzfd1nueG25R8p5nnaZK06ZPU2GWwUxYHgxHHAL/uT3/YiJE7y5juFRUuMfBpVRTNzzeFExsowtqJtpJxyvZvkhYeT+T5QN6yvEqJtgfmqbCCOWUvP37tmJPzLbUtljSv+fZWK9qfkshhJrm+7Xvq2oJx1EXglNPVFvrjZvh+v+oCx+okfBf+GTv8596Tq0va6qmhLNPL12R8dIrqgQum+29gCxbrrx/u49HncnC6+tVSeCnPlx67SPFMUeoUMuLL6v3MhhQMfD+dh+DoapSzb7rO69N16GhYWhDTD0mJRPf6ILKzA+UnZ+IvLh84Ay/ZSkDVg5uW1/TUlvTow5XRjLpkngKBpSC2EC7g5OOg79fo2qGozF4yym9W95Pf0Ql41ashCmNqhOu26hed6PyXLs91NdWw7IV8J0r3M9z74O9U3m7cdPyBXWObTvU9IvRRtPgFz9UibQXl8O0Jjj7jJGNtX7va/DT36qqCNuGow+Hb18xOXZuHiPC5JV2nAy89yMDj8AxDDVo89CCLWxHp2o4mDFVCfxc+w8l1ShQXm1ffD5V9eDzKe+wO8Sgacqz+uzHeqUdR5pUGk47v/iC4PfDf/+h4u+F/OTXqvqh8ILkNsTS71eqZRO9SmWwSKl+xksYyWN02aukHcvhocdUrLSjC044Wm1NC5NHQ6V7+9vdlmpaSguhtrq41ra1jASMZeU0a//Qe9sfr4O/3aDinalcFUK3geq2SYbem9zqG8c9+XglddjUoOKfhx8y2Fc4OHbtdjccfp9ah5vRPf+tKmFWOLDy1BPUWPS+4Y3zz977DC6oC4zn3b4p2fuM7m3/UzWQ3V/oO++D516C2/4xPLHzzi74/k9VbFkIFa9dtBD+er0ynD4/XP5xtQXv5qjDVJut7ZL578umLb3/f+FlVf/aN95ZiC83wZeC42ayyrO+5bqxm0c2ram4jhqU4Zw/1/05i/aFr34erspNdLYspXL2lc/B+y+C/96lwiSnn6yM98OPq3piTzHMYy9g7wsvvOXt7h7m7JkqxjjUTPT7P6bEYLr1E3RdeWN9375gAH7z417vck+rUhZLJJTH6vcp77RwW73/ol5P99tXquGJA1FVAdF48e26rkafj+UcuT//Qwm/dyfygkGljPaDr/f/vGxOoLyxoThuumWbEkjvPqZlwfe/rhKpHh4TnX7CC3tfQKmtw/32rdvhU19W42UGy8bNsHFLvmCNbRfHH9MZuPG/vb83NsAd18MVn4MPX6JqYWdO75WI7B4FfnmfKgBDH3jbGQrCeWe7K2/ZNvzjJnj7B4b2WofCRz4AP/iGKrk6+ABVbfA9t5rfAvx+JV7jlqj6yvfU3zKRVD+ZLHz7/7nXuXp4TCL2PqO7oB8FqkwWrr1+8Mfsig4sLdhNPJH/eyik4pIfuVQ1A9TVqDjnvDnwllOVoEzfJNr5b1UNAIX4fCp2GgqqioLLPwFL+ykz2rwVPvYF1RI8Fpx6Avzxl/C33yllsuEkiLqi6kJXeFHTDXhu2bCW6eEx3ux9Md2vfwE++SX3mlUpYfsO9+e157yqmdOLPc0l+xULwrgRCsI5JdpFv/hNVYvaHWsOBuH/Li6e33XwAfC5j6tWXl1TibqzTlPNAy2t6t+DD1Br/OKn4YOfdi8lAxXGeOjx/DhzuZiWamOurRn79lSfoao0ChGoC9Jra1Qcef/9BhYK8vCYYOx9MV1Q2gLf+wm8/Gp+/NRnwEVvzy/qjydUQ8CLLyvvrLoKfvJdpWnQl8efVlveksktnyrPuvLbxV7x6tfhw5/L7+gCda6Hb3f3ClMp2LJddeXVVJd+rdffDL+7tvS6TjoOrvru4JKIDz8B379KxZ9tC846XTVOjKWB+8I34Znne+t3hVBaEeEQxOK9Qj+//TEsWTR26/LwKId+Yrp7p9EF5bVe8nHV7ZVKK8+yukppw/YtH/vK9+Dxp/KL8yNhuP8WJR3Zl1dXKeNZKEYe8CsP+7wS42HuuBeu+nWx9+3zwQO3ltdhF4urcT4vvATz5sL736W8clCVFZ/6sqpccKtzPXypEiQvh63b4aIP5TcvBANw6XvgY5eVd4yRIJGEb/5IyXoKVNlYKq10IPq+xppq9R56Hq/HROJNV6cLynDe8Gd44BGlA7vfAtXO2teQZrPw6JPFRlRK1ap51mn5tx+4RE1U2LI1X983EulfhWqfue63h4K9Sl/9kUzC+z6qwgvZrPLg775PxYMXzFeG5+c/hP/7lBJ970s2Cy+/otppyxkhf8+DLhMuMmqU0Fga3UgYfvkjdbHJZtWO5OKPFF9UTFP9fUdKH8HDY5TZ+xJpfemebfaNL8I7zy/2XB3pLh0ppft2XQj41f+DGdOVwQyHVIXC76/qP9G2/yIVh82bVhuAz31M/f/p51WH1ro33J9/9wOqDK57TbatvL7f/Kn3MVOb1Jgh1/pcoaovyiGbdW9ddhuVNBZUVighHuHWikeuq6vMJKeHxwRg7/V0yyEYgEMOLI79OhJOOMb9ObNmwO3Xq6GStq2UsQbK1AsBv75STau972FlSN7/bli8EN51mfJObUdto884Bb77lfxk3iuvFceDpYS16/Jva6h3X0s6reqUy+GMU5Twet/knM8HZ55a3vNHi9kzVYhh09b8v1UkDAd4MV2PycPe7emWww++rr7M4ZAKEwQDapx3f23DQsC+81VnVbmlUT6fmlv296tVfPXow+H31yrB8mRKxVDTGdXC/MwL+c9dtG++l9xNYceXYbjX+Oq6MlZlrdNQniXkBNcNVb3x2WEO5hwJfn2lUmMLBtROY/pUuPpn5ZfzeXhMAN7cni4oha/br4dXV6ua1kMOGv4023J57Kni+GkqrfQHjjuq97bz36pGklu2eny3mLfbQMhSVQzlCHG3tcNln1EddNAryHLxO4pDM+PB9Gnwn7+pZJ9tq1rnMdIviJrNbHcytJbovRkMDbWwJJCvmhc1m1nRVqL0z2PScWI/93lGF9QXdzymy1ZUFLcsGwbUFFQzVFXCjX9Wot8vLlfjaj58iXti7MD9VZVF31i1z1A6EANxx73FIujZLPzpOiXzOBEQYvQU0wbg1aZDmB0c/ufk1apVzGxdTZWvVwxou5PhjXnnsyjt6Uvs7XhGdzy59GIlc1g4kcGtmaGhXrXXDsS3vgQf/IwyntmsCmtccE55erS7W9w95VKt1ROU1ZnSScOZmgrTbHf69yoLH9faATSMzPoKWZ3Zoo5fMzrH95hYeEZ3PHnbWdDVpWQokykVo/zWl3vrb4fC/Llw903w4KNK2vLow8pvHjjmCFUp0Xdwoqb1P7hyAtF3i/7GvPOL7g/7t0LLckB5rcms+7QO18fVwKLoyHmhK9oyNNQqY7tzP+VBLxrmyDmPycHe2xwxVGIx5W2G+hltM9I4jtKFKGdO2miv4/NfV+N0Uim1nmBQKaC56eKOMKszW5ipBfK23aUe50aPAYu6hwDWBmMs2HQHQL9b+XIfNxzWBns1MbyQwt7HsUtLJ9g9o9vN9p2qHfj1N1Tp1nFHK6WsyTB1eCRxHCUqs2IlTJuiRHlKJBZ3rangwV/PZ/f6CI3zk5zxuY3MOGDwAjtRs5lnVxusue8UeBlmLe7g1I+0Ujuj2PVbndnCq02HEO+cjbVRR5/moNf3foQHMmDdxm6kHufh4YZndAfCtuHc9yj92+5OM59PCWf/9ifju7aRYOt2uOs+1dl22snFo4GGQOumEH96/2GYKY1udRpf0OZD1y1nysJE/0/uQ9Rs5rnVBs999u3IJGALhO7gDzl8/KZl1EzPj72uzmzhwf+9i+jPgggdpAlTz4Il35aIMivHHBNi68BfA6EZZS91r0RK2HYTbLpWYHZB1QGw5JuSigUDP9ejNP0ZXS+mC2qwYzyR39prmmqKQ2dX/4IzE52nnoMrvqNKzWwHbrsHLrqwtxtuiDz991lYGUFfOTArI3jkL42c88MNZR9nu5Nh9cOn9RhcAGlrZFPwyF8aOP2rL+U9vu21Brp+FkSme8/b/IAksg/M/cDA52t9ClZ+XSAdkBZU7Q9LfyXxDcKhdbKQ2AKBBvDXlv+8icj2W2D9bwRO7v3sekXy4mWC4+6S+GvGd217K57RBSWu4oYmVN3sZDW6jgPf/Ul+d1k6DTfeCu863z1O+9oaNblCSjVC58Alrodu2xJGOvlXcyk1tuxq5J4G9+cAtBkZ6q38Ro/Uypoeg9tzLFtj/RvTyTbkTzdufmQ6sqDwwEkLdtwKcz9QetMGkG2HV77ca2AAulZK1vxAcNBV/T8X1Fuy6x5Ye6UAqYz2lLcoL1sbxiSo8WTTX/LfDxA4pqT5Xph98bgta6/GM7oAhy11n2PW1Kg0DSYrbe29jQ59MQxYuarY6N70X/jNH3vLxu66TzVgvPed+Y97/Bne0Xw5NlHWcAFP8i0yVCN8kmmHh/pNZB34enGCKnWAYNsqibR6v/zCkDTuX3yseFrQ5XLscuSOWx5zeZ4paHlUIh0QJXaE6WZY/X1B23Pk5B9617n7QUl4FsyfAA17Q8FyGcThZCDTWkLrwmPYeG3AoJS+fvANCARy7cBh1ZBw1Xcn98TWkoMcJUwtMLiJpBJOT2dUmMWR6v+//VP+NIw774WvfY/q3cupYwNH8Ts+xDGIgIm/DuZc2v8XtaFW/fRlzgckRgSETz1X+CR6GOb+X/Gxpp0n0Qo6orWAZPr5ZRiIUg/p56mOBS9+UND2PCDzwykATkaw/dbJ+xmpPQLQ8t8ALQT1x3gGd7TwPN1uTjtR6c4++6JqsT32SGWE3TAt1cK7YqXSAjj79PIkGseaYADefSH85/beEIPPp8RjDioIAWzYpDzgTMHe3ciNUj84Nxrot3/OC1cYZKjRt7L0gjup+cyFGEN4G4JNcMx/JFuuF3StlFQfALPfLwm6bDJqD4H5H5Fs/BMIn0qkNZwAcy8d+DyNJ8PrP82/TfgkjSeU9nLbXwAzCjilDascYNjzRGbRVyTPrxQ4GYmdAc0HU06F2jIaGD2Ghmd0+1JdVayhW4hpKiHzNzapWtZgEP70d/jXH1U4YqLxuY9BUwPccCtk0nDaSSpkUOjBT5sCpks3mmn2hlgcx1XDwdAy7F95Ky9OW1gytDAQgUZYeHl53tW8D8LMd0pi6yA0Xf2UdY56OPDHkte+AQhlLCv3VTHZUpgd9OsJC79k2jnlnX8iEpoOJ/xPsvshyLRAzSFQffDgNniOCfEN4KuG0LTRW+vegmd0B8u9D8EbG3unQKTTyjBd/VclyTjR0DQ1kv197+r/cY0NcMoJ8NjTvd5uIAAnHqtEgbqPNXumKkHrgzAM9jn6GDIty3muZvaY1Lb6qqDu8ME/r+lkOOkRSWyNMhKRfuaYgtp+SzcpYSHR/FCzFKacIXnlCkFigzJa8z8iCU4Z/NrGCz0EdUfCqm8L3rgahA7Tz4X9viLRS2z2uml9OlcNYqv3qeZgOPjnEuNNVt4+GLyY7mB5+vnisTu2Dc+/5P74ycT3vw4ffr9KsE2bCh98H/zwG/mP+drlyrvXcx+dUBAOPVjpEvfD1qpVPV1eAAs23ZHXlTWW6AFlLAcyuKBCHws+I9ECEs0v0UISLSzZ7wrJ0TdJFl4ueemjgpaHILFRsON2eO4iQbYMUbeJgrRV3LrjJcARSFOw6x5Y/b3+3d1sO7zyJYEVFdgJgZMRdKyANVdO3hj3WOB5uoNl1gyl2lU4SWEyVzl04zPgQ5eon1IcdRhc/0e4+TbY06Zi4W85peR+dG0wRti/lemvL2dpfW+Lb7S+mZ3+raxlbDzj4TDn/dB4omTPk2CEoel0eup6V3xeYKfJJdkAW2CnJFv/DRXzYeddAj0Isy6S1B0xbi+hXzpeArMTZJ+yPScj2P2wZHGCknH6lkeKb5NZwe4HJAf8cHLnoEcTz+gOlneeDzfdlm90AwH42P+N25LGnPlz4KufL+uhYf9WDmpZzpKpc4rumzlFsG7bCK9tEHT3YpZjHMKzYc77im+Pb6DX4OZwsoKdd4LZBU5KlV61Pi3Y9/OS2RcNe9kjjtmF68h7AdjJ0ka3ZJmeV/jQL154YbBMbYK//la1CEfCajDkT7+nJkF4uDKzsMZrnMm2wytfFDx8hOCRYwSrf5jzVodA1f4Ul1z5JZk93QYXQDUgvPEbgVNCY3606FwBK78hWHG5YPeD7iMBaw9TVSCFBJrA34+cZePJFBlY4ZM0lt74eOB5ukNj4T7wh1+M9yomDdudDKV71AaHlYSulUo3oWLh4L/cUsJLHxMkNqvttLRh110Ss1Nw8M8G76Lt8wlJ29MCO62aOzS/qjEmC05ho6OE9G4Ij5EG+447YO2PBU4GkIL251Xia//v5r9Ofx3sd4XsKacTOiDgwCtlv+9vsAkO+KFk1bcBTcWGK/ZR2g0epfGMrsewiZrNAK5C3MnsbF5tgtaCmO5ASAnxdcrIVu8Pmh923aeSO0JXX/DIXDj0msFpBERXQ2oHed1vTlaw5wlJtmPwWgqROXD0zZKtNwji6yS1h0vqj4ZlHym2VlIqvYaxwDFh3c/zW3ztlKD5Psncy9S6+zLzHVB/rKT1SdCD0HgKZelRTDkdGo6TRFeDr0YZXY/+8YzuBKHbcLnR11C5Pa5cQzbSdIuG79zvEHVDQ7HQ96J0JaT3Z+282bDpDhpqtxTNByskswde+oQgvRPQlDe76GuS1d9XGfJu4m8o3YSDf16+Z5VtxzWophmqCWIoAjahabDfF/PXUH8stD0re4yeFpTM+6BEHyOZ5kyrMryFCANirxcbXVCvY9a7B38uPeQ1UwwGz+iOI4UG1Dy4OC7se2VZv4/zvbJsdBZXJv2JhvdlUbqStfPOp6FTlY05lmDzzxrY+adKWmzB9PMkSw9+hPm/+zK3rP81SedYZJ+P56rvUpTskZZgz+MSKcsPM9Qsda+71UPD3/bH1sOaHwi6Vqk64vpjJKldYIRg9sWSptP7f76VVLoHI6Fc5q9zf0+6dwgTCTMGLQ+DFYOG48sr5ZvMeEZ3mPTnoZaDm6Et537bTmJZUYTm4s5MYPT2KKx8lBW378umFQ04aQ0b2HydQ5c1k2f4C7tZSqE7KoR7EmiwqWBfpfKa116pjidycsAHXilLtgKXQ7YTln1QYMUBBGYntD0L+35OMvs9/T/XTsGq74geQZ7wLNU5V1nGWLtS6AGY+0HJ5r+qsAIojYraQ6Fy4dCP240Zg41/FLQ8oi4wcy+TTD1z8MeJvQ7LPixwcs0Vb/we5n1YMv/Dw1/jRKVfEfPoC/8ey7VMGqp8U/OM7UCGcySRUhLrWkYysR4hdKRjUZOdyvT0QoRb3c8oEjWbuadhSVme7taqVRz285+x4NobwfCRTeokaeBvPEmMbiVxiWvtEqCHJY6pVMG6EX71RT/g+4NP3KR2wp7HlH7DlNOUZygdFe/1VStDMhi23gjrf50f/gAINElOvL//9a38uqDlYRVbVkh81XDCfRJ9GBOcpITdD8CWfwnsFEx7q2TO+xm2DKW04dmLBMmtvX8PLSjLusAU8sy7BIk3oO/fXQtIjv2vLLu9eyIyZBHzsTQmk4lobks/Hu9POrWVZHID4CClAwK6fM1sbzfJFMRT+0tcDeShj2SceG0wRuO27cy/9kZE1oSsSQAwSPI2PsS/uC/3yP4vGgddJVn9XRWrlJZqXV301aFlykPTYfZ7e39vew5e+6bASgAONJ0K+39PtfqWQ7YtVyVQgOkindgXOwO7H8q/mIDAsSStT6sLwlARAqaeCVPPHNlqgrbnIL0rf81OWrDhGtUEUm6ox0pCchMU/d2FOsfMt4/YkicUXnhhCIznxSiVXF8UlJSaxJnix4i8v+e2rVWraGhZzkyzuWeMeN962YFeQ7SfWPFgx5IvSlcy9Z71yIL9u47NfB4CHNzjBBLDZyIqfBz8c0ntIdDwkCS5WXmjgX70haSjuqyMyoE9u0wrrLg8P9Pf8qjEVytYdEV5Bqv+GFXBYPfVXNckdUdC1ypovkeAgGnnSqr6DGeWNurlF+KoxoSJSGq7u7KaFVdTNQbSa+hG86vEXuGxhK52HnsrntGddLhvW8yNBi9/WVB/tGT2+yAZVKVar6LKtsL+rUyZkT9gUkqbTHo7jpPBH5iGYfR6ym5GeY2VYvtu2Tu6vKb8seROKIzUioeY2fgo5eFG9D0cdG2EyP5Gz/wzzWDA+V17nlSi41YU0GDO+yX7fLJ0sm33gxQV+TsZwc47JIuu6P9c3VQdoH46lytBdD2ofioXSRWzzDVFbL9VsN+XJDPfoX43wlC5CKJrZJ58pLRVBcREpOoAXP9koWnlG1xQf8sZb4cdt/VWeaBJjDA0HDciS52QeB1pk4xwZF/lHvTBSvpY/5sj6HpVsPk6wXMXCxa0V5LMzmZ2dP8ebYM1VqrnxzKjtDT/l66OZ4l2vkTr7ruJx1aVPG9fg7soXdnzUy5tp70dUTA50iTECi6j+BvsoPssFlxZQ8VBobIHToKaXfbqFYJsq8DJKu91y/WC7f8p/Rwn697S6qou5kJyGzx1jiC6ip4St/pjJEfdJNny95wH7agfJy14/Wf5HvGB/0/irwM9ItEjSlhn8TclgfryX/dYUr0/NJ4Aeih3pdIlWlCtebAs/IJk1ntUzB5N6VMccd3kHX9UDv0m0toy5Q8Y9Bg74tFXicdWIYSGnXFY95ejee1np9FtvLSgVB/mAjXHblWvsH8ri4zH8FmFUlg6DVPOzfN4u1ljpVi3bdawxGkqVj7Pwq+9D/+eXUhbsop3c6f9J2x6s0V6haThWOWdVvcvXAaAlVBZ9OYHVNlXcBq0P0+R6HholuT4O90/6oktShmsbxJMGJKmU+GgnwxsSJZ9RNDxcv45tYBk8bckr/9YYMXz16JHJIf9UVLdJ//omEow3YqrWPVEH3gpHWh5FFoeEvjqYNY75bBLvQZT+jfR8aYB72VUVB1E2JhH+Kv/D9+f72GxtFjEefyPa0jRgJMWbF1rkgimShzBwSgyuIpMeidGxX6u94VzqmB96TbCye1q65xthcaTJU2nqHKsxBZVf1m5H8QPPIqX71qPr7UZU6vg6Q9WIXcDGUBTSavDri7P2EJvS29svVK3Akhuk64xUrvUW4FqFFj4Bcm6n4PwA44aze6WpJN2Lm4Z6l1Dx0sUid4gIbnZvUFBmhRNxdB8k2tLLTSV5Jty2sgl6fYWgzsQntGdpFR97Jv473oIkRuNux93UM86/sgKtLBk5gmtzJpVQtRVaogWHcjPYAgh0Eqk6xcbIZiSAnplwbbvlqxlNlOereTlTwqkpRoWWh6GnYdBph0SG1ViRGiq+qD+aIHZqMYLHHm9ZNtNSg8gPAvmXioHjNdKCV2vqC29MNTxZbbPt9UuHqgofJIpAzQmzHq3yvJ3rgB/vRKyEQIybbD5b4L2F5TBTe1Qc9Mic1R1Q+ViZTALhWyErl5T/TG5zrRMb61s48mlk4DR1bDln4LMHmg6TTLj7YOLk3pMfLzwwiREtHdSO+9YRCb/m56hguv1B+lqOJAP3Hgf/kh+ULJvcizaqWp9+xpeIfw0TX07Qit9LS5KpgHt51aR2FDgpmgypw3YZ8sdlJz4gCyrpz+fND7fapxUgmc/eBTxNwIgcrFYSdH4djSJMFSiBpTxO/zawU8zMKPwzNsFZrS7PCq/jlgPS2qPgNYnKQhnqHOdcJ+KTW68FnbeKRACmt4iCdSpeHHjyflaBa1P5UbE5wRqtKCkciEc8bfhNW54jD1eeGECIKXEzLaQSe9E00OEQnPRhlj5Ljq6QHfJLmmCg096iVlf3dWvwQWorD4UkCQTbwAOhq+OmtpjShrcwkRa7+uCh9yuzQ4UJsiEBq1PMKiZYprWSiT8N4Swee13JxB7Xe/TRABu4q3+WmVko6sgOF21/g5l67r9vyrG2luPmn8QOwmtjxffDqoioVuHdsEnYcEnJW3PqdI06SiveeOfYcGnVcMCwNqr8svWnLQg/oak/XnlMXvsHXhGd4yIdj5PKrU5lxLXiUdfoa7xLfh8g8+YOPNmISsjiGR+oNLvzzL/+qORdTUM1BwshEZVzRFUVh8GyKLKgkK6wwvbd29lay4C0W2A/XWM2niaYPBehEgjBGy7+wCcbGFaW4AulcOuq63+km9JInOHrzEQW1PcYVZ07hK3d7ysOui6s/DSgde+VWBUbXjjtzD1bFW9kNpefCQnq1plPaO79+BtWsYAM9tGKrWpTw2SjZQmXR3PDe2Amkbsb79AhkPIgB/pM5DBAImffRNZVzOoQwmhDWhwu1lshDhjRpgzZoSZOUUQ9m9la9Uqar+wAxHqE6YwJFoQZQz7IB1oOHHg86wNxthatYqtVavQ9W09XqoRcWn50iSNx8P0C2D2xXDUvySNJ5X1cpBSdT6t+o5g7U8EsXX591cfrEqhRoJ0MzldhnyETwmNCwFBlyZAYShvvXQQ0GOy4Xm6Y0A2s9v1W2OZbUgpEUPY+1qnHkvHmkcJ/PceyGTJnnc6zj5zR2C15bHYCLG4WzLhSxnemLeHp35cTaolwNQTBHPeJ3ntG4L4RpmXSCs3njtzinpPrOYgfhIALPzwsyz/9jnYqd5kn+aHfT41NHGYdb8QbL8VnBSgwY7bBft/TzL1Ler+GefD1ush2yZzIY3c31CjqCQtD03SeGJ+J5yvqsR4mz4auwu/pMbDO2lQXrTEScPKrwjW/lgJhjdM0IYJj/LxEmljQCq5iWjn88iCansh/EyZPgQB0wmKWy1vYnOuZGxR+UIr3cMsASqtdmYbT6JhIyWsvfp41l5zAnbKhxaE/b8vmXpG73PTLbDzdkjvFjQcr4yfmyOf2gnPXCgK4sOArsRWIrk8oRmFbTdB2/OCyDyoWiyJr4cdd+SHCroNsjCgajEc8lslWtOXVd8RNN9PT8hCGCoMcvTNvXoFHS8rDYj0LigMX2gByVE3SCrml/c+eowfXiJtnAmGZhHreinf6AqDSOXA6lyTnaHEVbuFzxWSXVUdTNNeR2ZM6g7ZQbApRmJLPdKR7H5QMPUMZfCia2HZh1TpmpMVNN8LtYfD0l8Xi7BEV6mtPYUzy2xYdpnghHtV3bCvCuZ/FOZ/tNc3kY6SctzzuERaoAVU0mzxNyXh2e4C4aDu99cLtt8qcbKqemHRV/LXVntoblCkS7zYycL2W8rXg/CYmHhGdwwQwqC+8WyiXS+SzTQjhJ9I5f6EIyMgbLrXI2hnH4gu4bkj90X2SWzJrKD1cUmmVW3R114psJP542k6luWy/0fnHzU0U9Xbup3PTqtx66UUvoSm9He7XlXx2OA0aDqZARXJNB/s+1nJvp/t/3FuYjLqDoHZ4RncyY5ndMcI3YhQW3/yeC9j0pLZ4QMfqnutD8KnxvsEGqBrdfHz7DR0vlJsdKsWq5+uFcUavtKGbFv/6xECqg+E6oNGvpOq8RTYfb8s6nLTgpKm05XRTWyB5vsAB6a8xX02mRVX4ZHgVLw63wmEZ3Q9RgTHkbTdE6T95gDrqwQzLpAjOvW28uCU65hwJETmq0kGQhZX7WoBpX7lxmFXS548V2C2FxveuqNKryXTqlTMWp9W8eJpb1VhgqHMP5O2Mp7NDwj8NTDrPZLFX5UkNgri63tfkPBB40nQdEpuQOd3cx2AwOa/qyTcrHeqxzomrPmRCq+ggVEBB/xAFl14ukm3wJa/C7peU514cy+VBKcM/rV4lIeXSJvEqD+dU3bJ12iRzezm/v+rZvv9+2In/QjDQRiCQ34rqRsB6eGtVauYOUXw0lXzif4kpPQMhOo4W/ItybRzYNNfYcM1Im/KL0i0AJz8qLtBtDNKZGbl1wQ4KmYqDJhziWTBp9zXIiU8+w5BYis9nXCaX9JwAkMa4b7ii4L2Z3MjdXL6Ewf8SGlXRNdA2zOgBaHuMOWZ2xl4/NT8MAqoJNtJD6lOuPW/EWy9kbxEnxaUHHeHLNJ8SLfAs+8S2EnVwi0MNUL+mH9L1xI2j/LwEml7GVJKkvG1xGOvIqWFrkeoqj2aQGDsvyW2nWDj42vYft8lPaVc0tKQFqz5ARx3x8jFICsvNll0QJDm+wRCU+NnupWt2l8oNLgAgkCDu8Hd8k9lpEEZ0oYTJFWLoeFYJc5Tiq6VkN5NXuuxkxXseVKS7WTQ4+DbnuljHB2Bk4a1P4amUyTVS6B6Sf5zEptw7cnQfCqRWHc4qgwuXRAycdTonu7ut242/73X4IL6105KNl8nhjyVw6N/vEjPJCSV3Eg89gpSmoDEtuN0tD2KZcXGfi2JTbS+PB3pUrea3F4sBDNcKveFfT8jWfCpfCnBin1UCVY+ktQOWPVdkaf2tecJeONqgZ1SP05a0PqkoHJh/wYX1DQKN6MnNGh5RB13510qljwQ0TUlztFeempEoB7XMItj9orouL3n0sZ1nFB0JUUXK2kJulb2s3CPYeF5umOAlA6J+FpSifWAJBSeT6Ry/yGHBZLx1UU1v0iHVGJ9TlNh7JAyS2RmHM1wir7URpXDtvrVpMx8vQY7Bc33Q2KToPoApbo1XNHq2e+TbPtPoSiN+nfn/5TxTWwROCnQQsWeoJMWbL0JGo7r37urOcRd3Fza8PrP1PH1kOCN38FRN/QvRB6e456E0yOUjA8HGqHhBGh9qo9ymV9Ss7S3VK3xZGh5SOYZU81QtxdStURNrcgzvLqkcknxYz1GBs/THQOinc8Tj76Cbcew7Tjx2Co6258a9HEcJ0O0cxmW5TbtUOLYLq7MKBMIzmLqSZsJNsXQfL3WSA+ZHP31dmZNzbcq2XZ4+gLB2qsEW/4hWPUdwYuXCdyXLtH1bdSwFc2th7YPoenkVMRcrJgl6FgmyO5RguLZPe7HcPrR3O3GVwmLv66mO2gBiR6SCJ+qtXVSAlDec7YNNvy+/7KG2sMgso8ymt1oQeXF91dtcOD/U9MWfDUSo0rJPy79Ze8xFn1FNV3o4d5JFAs+JV0rHOZcmgu/dLds6xIjBPMu80ILo8Wb2tOV0iGT2YmZacUwKgmG5vQra9iNZXYRi67AzLZiGNVUVC/F73ef0OjYaVLJTeQra9tk0juxrDhGmXqDUjq07bkP20rgpqwlhEEgNILlAmXiDzQSqVrIqbdcx2s/P5mdD+6HrzrLEVekWHxJhrUFNacb/iDItvduae2UIL5Bsut/hdNfM0Qi/0TXWgnhoLVJ5ujNwHmkdgq23SxIN0PjiZIpZyhPuf+yKFHw//yKBS0kmXZeeYZm+tug9ghJ6xOqqqD1KcGeRwvLzgStz/R/PCHg8D9JNv9dzWnzVcGcD6gkWn9oflj4ecnCz7vf769RXW5dr6pKi5qllPS4Q9Pg6JtUDLfrNUnV/srgTubx5xOdN231gpQO7a0PY5ptar8oDDTho77prej91P7YVoLWlrtz8dQcQqe+4S34/MWfbDPbTnvrg/mPB4TwUVN/UtnJr3RqK10dzxSHFXLnDwZnU1177JB0HEYCy4qSzexB18P4A1MQOQvYLQnZzcZTFmJuLVblbjxZ5nlrwcAD+P3LEKLXatvSR9uad/P0u/fJjWEX6CFJ1QFw2B+kytrfUDjOHAoNLAC68k61QE7b9hQ48IfStWXYzkBsDfhq3Dvs1v9asOX64tho1QGSo/7peYxvRrzqBRfSqS2YZmtv+4+0cKRNPPoK1bUlChqBZPx1ZGHLkLSJRV+lrqHYRTGMKqTL/BgpbXxG+bKOlhUrPm+O+oYz8Y3zzGrDqMIwqopuzxPGAW6ba7Nja+GTJaGZ6r/duguLeAVRMNlCEyap7SuxU73jJewUhBtfR0+sYv/Ph0m8cSptz/t7465Gzq8tuFZpBiz9jcSKqenCpVp3dz8Cq74lQKiPSuXCnK5Cn5c6812SbTcL7D7n0IIyr3U4vkEJ7HStVB1s+35G0nC8+zk99m5Gxeia2TYsK4bPX+f6RZwIZNLbXfotJZnMzn6fZ1qduA3hsl3jrCA0g8qqw4hFX+o9n9CpqDwQrc8cFtPsIJXcCFISDM8tClf4/PUIoRd5urpRPe4GdzAc8fUOdr8YxEr1egLCB7MuUgYq7N/KzCmCYKsfu6gEQJDZnj9G/rAf38mst67CiJhIKTjp7y+zZ9176Fw9DyerPFMzCis+r95+aanz+RuUeld4rmrNdTO6mT3w2tfzNXWjqyWrfyA4+Ke9BjU0HQ77k+T1nyjt28AUWPBZSeMJ6v50C7xwqSrNQgriMXjlSyoOW65OrpOF9b8V7LxdtS83naJit4WiOh4TnxE1ulLatLc+gmW2AgIpJaHwPKpqjhq3bW8pdD1CTqMv/3at/7Yif2CqkmrM88IE/kBTqacQqViIz19HKrEBcAiF5+MP9Lb8JBMbiXY+33PMZGI9FVUHUdFHEMfvn4LP30g2uyfntgkQGtU1R5b1escCVT+8hkR8NY6TxR+YQlXNkXnThWeenObsm3bz9Nfr6NhkEFycpuprDlsXOD3KYouNEImKRcS6XqLv+yzR2PLo0p7fq/ZtYda5r6EHLHY+tJBdjywk2BRjzrseJnDah+gbUjjuNhU3Tu0S7Lob0jsABF0r4OVPwuF/llQfkP96Wh6jKCohLcGeR2XR5Nrq/eHIfxSHEuw0bL4uV8bVp63XyQjeuEaNai+HVd8VtDzSq1C2+0HVtXbUjcViPh4TmxE1uonYKsxsK32/KOnUZgLBGQTHIcnTH+HIQpKJdci+IqdCp6LqoAGety+pxHpsO0n3uAKhGVRU9v88v7/BNdkmpU2s6wXyjbhNPPoq4fCCHm9YCEFt/SmkU5tJp7ah6SEikf0wXFwd0+xQjxEGwfCc3AVm9EnEVxOPvtrzWrKZZtr23EfjlAvR+iQo55yZZM6ZqhB1jdW3ZECoCRWo99mxUyQSq0FKNM1PTc3RhN+TJvqyRKYFtQftQNqC5z79Lpqf3Ac7GUDzW6z7y7Ec9ocs1Qf27iSCU2Heh2DtVd0bjr5jcWDjnwSH/KZgoGXpwRADIiVs/BNsvi5XI1w4xw3INA98HFCeesvD5MlQSkuQ3CqJriZvlLvHxGdEja7K0udv2aW0SCU3jZnRtaw48egrZLMtGEY1lVUH4XMxdrpRQV3DGUS7XsTMdqDrYSqqlhIIznA5ai+appJtqeRGzOxuDKOOcGTBkOeduZd/qYkOptlOQJ+Wd1soPJ9QuLSgajy2qo/h04jFXqG27mQCwRICBCNIIraK/L+/BGmTSW8tueZuI1uIEILK6oOpqDoAxzHRtABCCJZ8MIbpS5K9OkwqXkv7qzNpfmJBTzeckzUgC2t+JDn6pmIvMrm5OOEFQo1uL6DxFHj95wWP9EmaTh1Y5Kb5vpzBTZd4oKaGWpaD2emuCYw2sDCPx8RjRI2u0IxCmwsoQzUW2HaK1t3/g9yEsKydoG3PTnz+RqqqDysyvj5/PfWNZw36PJrmI1KxHzBA+1IZ6Fo439vOIaUzaA/VtlPEo6/QGzJxQEJXxzM0Tn37kEI8UjrYVgxNCxRdWCwrjm3FMHw16HoIKYtboaS0cewyCmBLIISOXjCEM3SyxSFHS9YGa2j/x3wcs9giFY7e6ab+GEnHy+TFaYUhqXcRuAnUq2kXr31dea7SUspii78xcEhg6w1uBldVUWhBVRu74NPlhRZCM5T+QuHbKE2lcuYxuRhRoxupWFI8IUHoY6YbG4+tApeRjGZ2D22tD1JXf1q/sdeh4DhWzuttxeerIRRZgDaQsGofND1AKDwvN7Sy+4ql4w80YfgGl4Q0s3sQQisy4o6TxbGT6EZ5Rlw9X5DN7KKz/WnUTDeHQHAmNXXHAYKujmdIp7blzmcTrliE4WvIxfP7IvCPmiaEQOw3Ez3oYMXzDW+p3OKMd8CO2yDdLLFTygAaFTDvw+4GsPEEOOkRSWydqn8N9b8R6sFxbQMW+Osks98vmflOyh5dJHQ48EeSFV/IjfyxlTDPvpfLIq0Hx4K2p5X0Y9US1YDhxXwnFiNqdIOhudhWnER8VW72l05VzRGu9aujQTq5sfSd0iYWXU5945kjdj7HydLWcm9PfDed1knE1wxY69v93Hj0FdKprYCO3z8Ny2qHXPJxoNiyG1rJJKBElHEhyGZa6Op8DtuKIoS/R9uhm0x6B7Gul9GNStKpbShjnEv+xVfjHuyUaEPRPCyTzJFxgrWQTEucXNhAC0rmf9zdiBph1Z7bfJ8SIK9YKJl+Xv8GUPMNPm467VzJhj8UthtLsu3wxu9Uknn+B8s/Xv0xSjxo94NKQ6Hp1OKaYTMGL14qSO9WWgyaodqWl/5aUkbPj8cYMbLhBSGoqDqQSOUSHCeDpgV7iuRHG8fJFjUgFFIqfjpUkol1fRJqgLRxZIZE7DWqakoH7KSUtLc+iGV20R0KyGZTVFQsoaLq4LzHqfHopd/DbLaVVOINpLQIBOciRAgp4/QaS51QeN6AIR7LitHe9nCPt+0WKgCbVHIDul6JaxzJpVMOBKnkprxKDDf6NlGcMSNc8ra+51qcsVkfaGDKLW+Q/O1U2h6owKnSWPRBwbSz+zxSwq67Yeu/VLvxtHMkcz8AMy4YvcaF2e+Fjpeg7XmJeisFPRclBzZcDbVLJbWDkMoINsGc95W+f9O1guT23uYQ24SO5ZLdDyjNX4+Jwahc/1QcrvBLMjS6W3UtsxPDqCYQnNGPEeozsdUFn6/8ZoRyyGZ2UWx8HDIDpKXNbAu2FSOvXE3aJOJriFQeCEiiXS/lSsxs/P4pVNceg17QMpxMvEG068UeQ5lObaav2IvQ/ITD+/brNWezrcSjK1XVSck5MX2WWVgrNSDOoGK63VOA+7stInYTqPwrfpHgECTxhibsq48Ezce6bbOYls53WzdcA1v+2Rtj3XQtdL4Mh149ekZX88Ehv5GsvQq23ejyftmw805B7aEjt4aWR4q78ZyUoPlBJYPpMTGY0JsOKS3a9zyIZXUhpYUQBrpeQV3jmUWem6b58QemkM00U2x4BULoVFYfNqLr041qyLQUnW+ghhC7hHiLlA7SydLR9jim2avKks3upm3PAzROvaDngpNMbiHa+ZzbUdQ/Qqe65kiCoRKtVijx8fa2R8oytgqNYGgW/sA0Yl0vurckFyCEMWBFCBR3rrndFnVgR9ZmkXErhuj1xKtoIRBbQXN18e7CTsGWf+Q3ODgZQcdySWw9QxrdPhiMSD8XqBGOtfpqIbW98FaZq0keHRxTTXv21Xqx43KZ0Cpjyfh6TLOz58stpYVlxUjE3YVIa2qPw+erB/SeH8NXTyiyL/VN54y4pxupWFwszyh0KioPcH9CDp+/ETfJC00LkMnszjO43Tgyk7ugQDazh2jH0/0vTtokYi5Dw/oQ61o+gMHNjQoXPoQwMHw1hCsWYVsJdL2cViiNYHD2sBNptoSfdcAFu+CxjjayorDawynRYahUzVz1b3VIFrYjjwJNp0mEm2ujwYzzR9b7bDpZhaPyESQ2l6fvOxikVDuIx04SPHGW4IkzBXueHNlz7K1MaE83nd5O8fbdJpPeRqXLllnTg9Q3nYVlxZHSxDBqRrUTzjAqqWs8k1jXciyzvUdxbKDEoeGrIhTZh3RyY+6Ckusuqz2aWPRV9ydJBycnWJuIr8atFbkQZxgxbiEMNC1EbcOpuZKxIKbZSfueB3Pn7s9gCAKBmVRUHVBWEvXBHb2K3TOnqAaJbFxwzzeq2XVzNbYPNl8Uxf5UJ/jsEg6im8GBQJNKKBW+W9JU429Gm6pFMP9jkg3X0LsIAft8QmngjiTBaSD8UBiOF0INqRxiKbkrO26Fzf/oDdlk98CrVyjFslI6Ft04JrS/qITa644qv4pjb2FCG11dD7kUgIGm9R8vLlcucSTw+WqpazjV9T7L7CIRX4ttJwmGZhIKz+/xjKuqjyAYnEU6tQVN8xMKL8DwVRHtXFbiTLKndbi8GKlOKDR3wLVns7uLnhcMzSIYmtMTPzeMShXqaX0A9wRaPoavjpr6E8pKoq6xUiSzSuR8bTDG9t1bWTwD7r5wGrteCCAz6hgL/lxDYLuP5T9LoxcYV0cKbH8dbi6l5oP9vixZc2VucoJUymTTzmPM5AvnfxhmXChpfRLQlG6CEVHeYko43BBs4yVfAoHgCDPMxel6gkPYhNYsdc9q+GpgpAuItlxfXIfsmLDjNsHCz5e+ICe2wLIPiR7PW1qw/w8kU88Y2fVNZCZ0eCFSsaS4FUfoA2bCJwLZzG5a99xDKrmebGYHsa5ltLc+3BNWEEIQCE6juvZoKqsP7anJDQZn4bYfDobm9iQnlW5uf1MnNHz+OiIDyP9XVh+GEEaf8+noRgXVtccQDM3KM5qm2VneCwcss4321odcmz76Uij72D1d4u5HbZqX9RpcACOtMfueCJmOML/lWDJSJyN9SOknSyUbzCPyjtWX6W9TurXTz4MpZ0gOvFKO+fyvQD3MuADqj4JXrxA8dITgkWMEt1+V5mUngSXAFJIXfAmuDrUM6RyhaTD3MokWlCCUuLoWlOz//ZHXZ7ASLjfaKr7bH69eofSU7YTATqhY+6pvCcyukV3fRGZCe7o+fx21dScT7XoR24qh6xEqqw8f8QaH0SDa+WJejFFKG8tsJ5vZRSBY2sWKVB1AOrM9J1aujJYQfhzHIp3aSiA4i0jFfqRTW7HMTkp5njV1p+YMaml8/jrqm84hEV+DbUXxB6YTjizs8cYzmebcxIsEPqO+rMRZN5bZTia9nWBodsnHbN8te7zcbpLZ2aS2GUiXa4pjQLBV5/nauaxlBl/KZJhhV2Hbs+gKxvOOU0j1gVB94Phm8KUNL16m6mhxBE4Gam8LszTdyIs/U3F8S8A6I80LwU6q+r2wluDz0Hi6TvIhA61CEj7XZM9USYlhGUPGf3aQ7E1+6FMtoYcge06CtUH3z6TdIYhvqswT/gGQBqx8KU34rf2HwyYTx1I65zGhjS5AIDiNxuDbxnsZOE6GTHoXQugEgtMHnG9mWcWXbiktTLOtpNHNZJqJdS3HsdMYRiVCC2Nmm5EyQzaznWy2mVBoDtW1x1DfeBaJ2ErisdcoilgKgXSSUEayyzAqXZXKMumddLQ9TrdRz5SalFgCKS0ymeZ+je4ZM8I8uGMra+k1vGH/VuadafCUtV9xhFaTZOZY+CScmGlgara255LTn8GdKLQvQ3l0fYZ4GmmN2f+L8PL3W7HD6hX7NMGUmTDHP8SN6HwJb+s2YH3qg0cQ6xdZlq00SL6h4TgSYQtCF2YJHGOzaL77uq0Y7BLF4Q9Ng1nzoLHE8/Y2JrzRnQikklvp6ni6T1JOo67h9H51bHU9gm0XlIYJo2Q5WTbTQkfboz3esWVlgc78B0mLVHIz4cgSDF8lwfD8nNEtQNrYdtJVgaxcYtHllBO/LY2OoQ/cxjxzimDdtvzbDprix/l+G898p16VemkSwwezf7uTc0UFx8VrqJQ6zQ/AhqtFz0ia/b48cBJnINqFxTO+OHFhc7AVZpEdRIyQ0eovQmMkNexw7/s9wzd2X821GwdOyrpRfUOc0Es6jZvCVB8kiczxsVak+z1e4EST9BM+6FZMExJpSFr3MWnrp6F0snHsotL3eUZ3ABzHpKuzW3+g9/bO9idomHJ+yeqIiqpD6Op4hl7DpaHrIQLBma6Pj8dWllkv69DWeg9IG92oyhn34kBaPLZyWMpitmvQrnyEEIQivcpiUqqWYTddirBfebsA3SnSpZ+Nkj2uizV/m4k/2MVZH8vQPC+K3FZFpdTZ/SCs+k5vMqftGckLlwiOu7NYj6Bc1ulpfh3ejYPEAp70xzk6G+GSjPv8u8FSe7j7JOHUVBun3sYHIOBDdZUYwwjCdhu9Uh6nG0PeKRyQ+ynzOAu+A699C1qfzonWz4KDroIKpxJGuKxtorJXGF3bTpNMrMXMtuHzNxCJ7DdkqcVCspndCDRkgddn26l+RWRC4Tlomp9E7DVsJ0UwMJNI1QElwxKlGiaKkT3GWU2rcP9ylppkUS4+f32u464v3VtVJYiD0HIKLMW1oZU1R6FpfqS0iXa+kJP9lBhGNdV1x+Pz1QA5accpKWBbn3MoKg9OU/PFDGF/C7UzwjT3MVhvXFOQPZcCJyvZdTfMef/QXvM/gq1kRe9rySJ5xh9nnqbTIIf2VenCZpmeYrew0Cug6tYA035QTf0rQZUjFnD4P9NU1kQQQnBoyE+tPoRY7jBZGxwgAzZSBCF4DUyPgcwI9AZJUT/HXsCkjukOhG0naW35H9IxAYdsZjepxHrqm85FHwHDq6YDuyVg5ICJqkBwWp636dhpOtqeIJPekdPGXUBl9VKE0PEHppJK9tVMgF4DNFACqLhQyPANr0aosvow2vfcl6tAcFRrt1FNReVBZNLb0LQAofACYtHlZNI76FuEqmkhQrlOuGjnMlLJzT33W1Yn7XseoGnq23smL5fS1AVYOGsbbheWbKGYGarTLLUTSr1f/RkWE0mLVuyGCgFWo82iivKV47rZYVr8vqWLjJS9K1qSZP0NSY5bW8nJOytousDCVw2zGJm2eRichzuUx48sb742tklvdBOxVT0GV+HgOFmS8dVUVg9CTaQEfn9TTnGr7xdSwx+YmjfjbCB6RG6sKCCR0iaZWIfjZKipO5aKqoPIpLfjOFnA7ml5DlcsJpVYhyNNbDvhOtcN4evV/OtpeT5kWK/b56uhYcp5JOPrVWVDcDqh8DyE0AmGekMk1bXHEu18PqeWJvH5G6iuPa5HYjKVVCOK8nFIp7cTCs/tdw1uxtjuEKz7g1Avt2DKrx6S1B3Za3DdjGwpA+NISWCnIF3QKagLQZ0+NKP0365E0fFAJfyfWhzjvFP9+IZ4bI/Jy6Q3utnsHty+1Or24SOERl3jGXS2P4Vlqp7SQHA61bXHDuo4ZrZVGc08L8wmndqM4xyOrodomHIeqeQmLLMTf6CRYGgOQuiEI/sA0Nn+DOnUpvxjCIPq2mOxrSjZTDOGUa20bUegQUSV6C3t9zGa5qOm7vhczFbmjeUp1SUmkSUV4aS0Mc0OdC1YJPBjJwS731mBs6db2KX7+KrhoWYpPcMguynXi9OE4KzKEPfEkmRzS9aBSk2wf3DwXi7AlmzpEihDCDZnTQ4KlX/h9hh5Eo7D+oxJpaYx32+MySzHSW90fUYNltlB4bbcyMUMRwLDqKSh6WwymT1kUlsRQse2k4MSK3ecFO5bKaE8dc2PpvlzEymKkY5FZdVSzGwLjpNW234hCAVnEwzOVB+WcWwaEUIvKsAXQsfnb8AsvABKCASKy+ZSyS1EO59FDTV18AeaqKk7qceQ7/p3DU6H6KOkpf7110uWfFuNNC9sguubSR/IAL+1MkxYEzwQS5FyJAeF/LyrugJ9iF/EaT6Droy74XWQ1BtjH7sdDpuyJvdEk7TbDgcF/ZxRGSKsTV5P/cl4ihs74+hCIJHU6TpfaqyhapR3H5Pe6EaqDiCd3poT01ZejxAGkYqRNUDJxPpci676Eifia6iqOYJwZEFZz9eNGtfmAk3zo/Ujg2lm2+jqeBbL6kIIjWB4IYZRiWV2EAhOn3ADPwuprj2W9j339xEtklRWH1qUgLSsOF2dz+SFT7KZ3cS6llFdezQA8ZVBZKrYADpZaDyx9/ehJoWEEJxSEeaUioHjq+2WTbNlM82nl0x8vb06ws/2dPZ4zt0YwFyfMaZlYcNldTrL79u6el7LTtNiWSrDt6fU4puE8mKtls2NnXFMwMyFgHZbNv/oiPHphtGdaz95/uolMIwq6hvPJh5biWm24/PVU1F14IjqLziOSbRrGYUTe6NdLxIMzS3YUucjpSQeXUEivpb8hJeGEILquuNKbmkcO5NrpzVzx7JJJdbQfWFJJTcSDM3siaFORAyjksapF5JJ70Q6WfzBaa5ay5nUViiKfzqkU5t7jG714Sl2Xi+LDK++n83aYH6J22glhxwpub4jznPJNIYQmFJyXCTI+2oqiv6O8/w+vtJYw11dCTZkLbJI/EJwdDjI+VXDn9CccSSaYEyM3s2d8byLhwV02A4vpzIcFR5BJZ0x4pVUpug2B1iZzuam3oyiUNaoHXkMMXzV1NQdP2rHt8xO17IxgYZldeD3N5Z8bia9lWTidfINtkYwPJfKqkP6HeuTTm1BuqqJ9cZE06nt+PzrS4YlCnGcDLHOl0int6r5dTmR89E02ir5NnyPvOkdXaz7yTSsnRqkBcKQaH44+NcZqscoA/9cMsPzqXSeh/RsMs2+AZ+r8Znt9/GpxpoRXcMey+ba9iibsxYCODwU4JLaSgLa6BmKFqu4hjwjJTvM8lvDQTkhHbZDSBOExjE04RNChcMKrvNjEfDZK4zuaKMm3ZaY2DuA4lkysd4lrODgWMmB56jJbK4qoT/UCJ1yjK6qoHg4p9nggLRIxNfgOCmqa4/BsqIkoqswrU78/iYilUsGXONIEQjNJhZ9peBWjWAfpTQ9KDnhhSTb/uSj7X6D8AKHOZ/LEtlv7DQVnkqki8IFWaluHwuPz5aSq1o66XKcHnvxUiqDjeRj9aO3LZ7q09lm5hvegIBZgwiRrMtkubY9RtxxkBIOCwW4tK5yXMITh4YC/LsrvzbeBxwTCY56Mm3C7EkdxyQWXcGe3XfStueBXO3nxEA3KggEppJ/HdQJBKcNOGHXTawcVAZ/IAKB6cWZIRdEmddny2zLaUL0NeQ2qeQmsplW2lruIZXagGW2kUy8TlvL/3BGWv26BIZRQXXt0QhhIISP7onIhdM+jEqY90WTwx9IseTqzJgaXIBSzuRYpcTWZkzSMv/TYwEvpbJ0uXijI8V7airwi95UsA9o0HUOKbP6Im47/Ka1iw7bwZRqzS+nMvyns9ymoJGlQtf4XEM11ZqGXyjv8+CQn4tqRl8WdkJ4usoDe6BnUKNNlI72Nqqqj+wplxpvaupPJBZ9JVd3CqHwPlT2GSJZinBkAV1mW37/pzAIheeRyTSjaYGSYus+fx2RyOLcpAyJWwmWEAbhMkMLtp0q0WrsEI+uKPDIHRzHJJlYN6TJxEMhFJ5HMDgL0+xA04MYxsQTsTklEmJT1szzdv0CTq4Ymx1BypGuF2wJ/LsrzkdHydtdGPDztcZa7o8nabNsDg76ObkiXHa78kupTNGqTeDpZJr31o7P33lhwM9V0+posx3CmiAyRuGOCWF0s5ldroMa49HlOeHv8c+OCqFTVX0oVYNsuAiG5mJmW0km1iOEjpQ2fl8T0c4Xc3FUia5XUNtwek8HnWV2kUpuQmITCs1FM8LEu5bnjKJ6jjqWJBxZ1O8ctL4YeukPt2l2uNxqY5ptro+XUuI4aRwnja6H0bSRqTcVmoE/UDpGPpY4UrIha2FJyYKAD1+uTXe7Geb+WBJdCGwpObMizNIxqrddFPBhlXDul6dGNwk002/wobqBRYzcMKXEcVm3JRn1xFV/aELQOMalexPC6FpW1DVm6jhpCruOJhtCCKpqjiAU2Y9kfA2m2UE2uxMgV+amZCC7Op6hruFUUsnNdHU+26NpkIy/Tr6HKwGdisqDCEX2HXC0el+0ku22OoZR5TKbTcfnKxZ7yWZb6Wh9DCm7Qw+CYGheLjwwYSJWw6LZtPj5nq68jrK3VYU5LBTg/OoIb6kM0Wo5NBoawTFMCFXoGkeEAjxXIvs+Ft8WR0oejKd4IJYk5UgWB/28t6ai37rjg0IB/tuVX2GiAQcG/RPCqRpLJsQ3xOerc/2y6npkr/gSS8eis/0xUsmNWKaLaACSbGaXKk3rfD4XAuj+srsJytikUpsGZXBBDb70+6cU3S6ERlXNkQVTJDQ0zUc4sjDvsY6doX3Pg30Mrlp/OrWJhJvM5CRESsnv26J0Og5pKXt+bu5K8I3mdq5rjxIQgll+Y0wNbjcXVkeKvCUdOCDoRxsDA3ZPLMmd0QRRR2KiyqyubOnsqeZwo8nQeVdNBQYQFIJAzsO8ZJxCC+PJhPB0ff5GfP5GstmWnMFRClZVLuLak5FkclOuBbj/RIdlxRhY3Eah9CYGT3XdCXS2PYZpdiCEQAgftfUn4fPXqikSsVW5NuQmwhVLivQl0qktJV6HJJlYP2bx39GkzXZos93/VhbwQjKDTwgSjkNQ0zgpEmSOf3AXwOFQZ+h8oLaCf3bkd1NdOgwDtjFjsiyVwS/gmHCQKS5VCWvSWW7rirOpoIpBosrHXkllOTzsHmZxpGSB38cVTTV02A6VmsaCMWq7nWhMCKMrhKC2/hTSyU2kUlvR9SDhikUjPjJ9vDB7Lial0JTOrmP2hBz6Rys7jluInpuYbFtxpLTQjeqeD75hVPY0IpSivwnD7jXFEwNTSl5OZWi3HBYEfP1+4XW36Y59jwU8nkj3bOWfT6b5QE0lR0XGrkngmEiIg0MBNmRMKnSNub7i1+NI9RcpTHa1WTavpLP4BBwSDPBIPMX98SSmVFvfB+MpPlJXlRenLuxIK8SSkq4SF6pNWZPftSq1NQeYZhh8pqHqTWlwYYIYXVBb3FBkH0ITpFqhXGw71aOwFQzOyishs+0kXR3PuujS9kXpE0hp0d7+iMv9GkLzK89WqBkGulFFpPIAl8eWT6GYTLkEgjOIR1/BbQT8QNOHx4tO2+ZHuztJSVWuZAgVS/xoXZXrdrxW15npN9iStUpeRvpG2LMSbuyKc0Q4MCbb+27CmsaBLgk8W0pu6YrzeCKNJWGez+D/6iqZ5jN4OpHiXx2qTEsIuEnGsendu9iALeHvHTEO6hOu+G9XoqTB7T7Wfi7CQKaU/HJPF6k+oYftpsUf26J8pWnvcKoGy4QxupORTHoHHe1P9HwDY13Lqa49hlB4riqD2/Ng8cieboROVc2RBAJTSad2EitqMwbQCUf2paJqKbYdw8y2YRiV+PxN4+Yl+Hw1VFQdSDz6Kn3dQcNXT0XV0nFZ00D8pzNB1HF6DGhWwmvpLKvSWVejBfCp+mp+39bF1qxV1tCirJR02g51Q8yE21KyOp0l4UgWBX3UDEPI/NauBE8k0pi5P88m0+Inezr5TlMt/+pQegNAv958VkrabYeG3OspFW4BVTJ3QiTIzBIhicISNwfYnLWI2Q6Vb0JpS8/oDhEpHTrbny4KG3R1PksgOBPL7MgpixV/sv2BaVRWHYzPryoD0qmNuMVJfb5aIpVLEELg89WOW7hFSodEfC2pxHokDqHwfBqazlN6CjKLPzgTfz/z4sabVZlskceakfBqP0a3Wtf4elMt7ZbNQ/Ekj8aV1oKVa0wo/GsJGJIB2WFabMyY3BFNkJHq0+JIyTuqI5xWOXhhc0dKHk+k8rxSidr+PxRPoef0IgY+DlT0SRLu4/fxajqb92k2UDuGsyrDzA+4x7TV4weI17zJ8IzuEOlppS1AoGGZbTiOiWvxjtCpqjkqT5BHCHeJSNNsY0/zHQghqKg8iEjlkgHXJaUkm2nGMjswfDX4A9OG7RX3jttRpiYRW42Vbae24ZRhHXesqNA0Ek6+mTSAmjKMZJ2h8+6aSs6ritBi2dTrGte0RdmUtXo8Rr+AMyvCg2pnNaXkd61dvJE1sWTxJ+nfXQlMCadWhvCXcdw16SyPxFOkHMc1DODI7sJDd+NnoJKEAH7guEiQYJ/2u3dWR1iXMTGlmh/nFzDdMPhofVW/DRKLAsWfbQ3VPjwWXu6qdJbbuhK02jbz/T7eVR1h2jiru3lGd4hoesC1xVfiqC4zX61r7bEmAuh6futwpGIR2Wyz+1SI3EDMeOwVdKOi35HmUtq073kQy+pESgchNAyjmrrGMwYcLVQKx86QSm6ksHU4k2nGsmITsmuskHMqQ1xfoJKlC8Fxg0h8hTStZyT65xpruC+a5PlkmoAmOL0izDElsvaluCeaZH3GpFRaUgK3RxM8mUzzjaaafnVrH4+nuLmr9/WV8itPigRZmc7SYtk9f00fsDjgo87QWZZSVRknR4KcVeBlT/UZ/GBqHU8kUuw2bZYE/RwRDuQZ3JeTaW7tShBzHOb4fVxaU0GDTyXNft8aRQ1+koSFRkgT/Ka1i+MjQQ4ZpVrdNeksV/dJ/q1MZ1mfMfnB1NphhW+Gi5ClxAGAtsyGsVzLpKO99WGymd30GiQNn6+O+qazAEgmNhDtfCF3n1I1qq0/FX+gqehYifg64tHlPTPJ3L42Pn8T9Y1vKbmeRGwNsegK8je/OhVVB1ExRIFz0+zI08PtRggfNXUnDmvi8GBZY6XQfEOr2ng8nuKuaJKo4zDbZ3BJbYVrmdcey+aWrjjrMia1usb5VREOHoVus6/taqPVHrjawwecXRXmvBJSkJaUXL6zzXUskF8otUyJUiJ7d00FEpUkey2dRQOODgd5T03FsBXKHool+HdXMu82HfjR1DrqDR1LSjZnLV5Mpnkq2Ssa5BdwUiTEu0dB8+DHLR1syOZ/bg3grMow51cPX1qzP471l3ZGPE93GNTUnUis80VSqc0ABEOz8mqLw5F9CASnkkntgJy8YalpE5GKhYQjC3CcDJ3tz2BmiyseBqrNTae3UhxttEmntg7Z6BqGe9unlPa4xZgdKVmRzvJKKkONrnFiJDTgFIaTKkKcNIA+QsJx+FFLB0lHbcLjjs2f2qNF5VMjQbmaBSYq6VfK6EZtB8flAh0AjgoFeC1tEnMcVqSzvLSrjQurI3ymobpnlzYSHqYjJbcWGFxQn8T/dMX5eH01hhDM9On8IpHO8+6zEh6NpzizMkz1CIcb2qzii5qFu0zlWOIZ3WGgaT6q646lSh4DuH+AdT1CuGJh0e1uCKGh6yHCkflEzZaCml2dYHjeAOtx3y4PR55RDbk8rM/UDAlCp6LigBEbcz8YurvFXs9kyUjlTT0cT3F5Qw37lEjmlMuziTRmgYJXVsLtXYkRN7qnRILcGu2/DAtUqKBG08hK6RrbrdI117ZfKSDqSLocB5te7d/bogkWB/2ulQZDJe5ISqnqburjabZYjmsizycEO02Lan1os+hKsV/AxwsFQjsBAUuGOPNupHjz1WuMAqqza+RiUsHQXALBWYCuYrFCyRwOpJkbqVwCosDjEzqRioETcP0RjuxLfeNbCEX2JRReQF39aVRUHTisYw6VdVmzx+CC8qYyEv7VOfCIHikl6zJZbu6Mc3c0QVuBx9Ni2a5GsD0XBpBSsj5j8kwiTfMgxbsLObkixImRID6UIQgKwbmVIXwFHyOJqrL4/M5WbumM4xQYLEMI3lYVwd/neX6hElivZ8yifY8l4aVksW5DX55LpPnKrjY+vn0PP9zdwaZ+BmwCRLTS4qI1fWLRDYaG7RIGsaRkyiiIzlxYHSGiiZ73JiBgqmFw5CDj7yON5+lOQIQQ1NQdj2V2YZrtGEY1vjJKsvz+RqprjiMWfQnHTqDpYSqrDneNIQ8Wn7+ean/9sI8zXDZmrJ76075sNwfeMt7cFeeJnAi5AdwbS/LZ+uqeov5FQT/PJNM9Bh2Up7lPwEfakfxsTyfNljK2DioeeonLmJ5y0ITgoppKzq+K0Gk7mFLyv1iSiBBqKgUSMxePtQAkPJpIUatrRaVkb6kMM8XQeSieIu1Ijg4HOKkixJd3tRWlBjTIM9CFrEhl+GdnrOfis8W0+PmeTr43pa5kCEcXgnMqQ9wZSxXdt820eCNjsiDgI6xpnFIR4rE+JW1+oeLNQ61v7o96Q+eHU+vURdKyWRjwcVgoUHZoZ7TwjO4ExvBVY/gGp48aCs8mFJ49rnJ5o0mDoeETgkyBx1Q9gPBMs2nxeLw3nthtyP7WEePKqXUIITg46GeOz8cW0yQjVRLLEIKLqiPcFU2ww7TyttEvJNMcEvSXrPUtRdR2eCSeYkvWZH7AxwEBPz9v7SKbC20IlHEsrELISngonnKt3z04FChK+J0QDvJQPJUXQ9UFHNnPhIu7oskib9+S8HgixdurSye7zquuYHXG5I2CxJWJEsj5bEB9jt9ZHWGW3+DReApHqqaK40exfTqiaZxRZr3zi8k098aSJB3JIaEA51WFR2XasWd091L2RoMLsDQU4JauBJbdO7HOL+CCqv6/WBuylutMrE7bISUlYSHQheALjdW8nMqwJmPSoGscHwlRpWssS2WK4pYZCS+mMoMyup22zfd2d5DOxUHXZkzuJYnVZ2luzRfdZMtobOjmbdURuhyHF5IZNAF+IbiwKsz1HTHWZy2qNMHbqsIcHemN+Xe6JJls1BDKgSjlQXb06WYTucGcR0+wYZaPxJPc2qfV+bF4itXpLN+ZUjvird2e0Z0gOE6WVHJTTuGrkWBoDqIwPuuBTwi+0VTLbV1xVqazVOoa51ZGOGyAOF2trrkmMIycMepGF4IjwkGOKDAKQZcvngDCg5QevTeqNGi7zVB/keHCa4QBHDEIA28IwWV1VVxU4xB3JCEB32ruIJnzqPfYkn/mxuUcHQmxNWsSdzHqPuCgMpJPBwf9bMyYZAvWXM5zxxMpJXd0JYumHbfZDqszJgeM8Po9ozsBsO0UbS334DhZVInXJhKx1dQ3noXoZ7z7m5UqXePSQU4wWBRQegZ7LDvPQz69zJEzb6kIcUNXfoOFT8AJFYPz2N7IFie3ShEC0rnzgFLnumAI9aVhTSOswcOxJCbF1Rl3RZMcHQlxU2fcVeDHAZa4dJYVcmJFiOeSGZoti4yEgBDU6BpnDqGdeSyxIE+QpxtHSvaMQnmZ942eAMRjr/aZkgFSWlhWjGTyDSIVi8Z3cXsJmhB8pbGGW7riLE9lCWqCMypCnFbmbLNjI0E6HYd7Y0lsCWFN8IHaSmYMsvSqQdfZ6pL089EnaZYjSe8X9EO1VSwN9XZuvZbO8lQ8BQJOjIRKlkElHIf1GZNKTaPNdq/O6MrN0dlaoiJDAi+m0pxc0b/x9AvB15pqeCWdZVvWZJrP4JBQYFym/Q4GA6jXtaJmFSFgnn/kTaRndCcA2XQzbtMhMuldntEdQSp0jf+rq+L/hvBcIQTnVEU4szJMypFENIEmRF4HW42uccEAHWyltA+OjwSp0jVeSKTZbfcqolko3YRX0xkOyYVQ7uhK8EA8mdfe+tbKMOcUNFA8HU/xr85eofOwUJNv+xpeAeybq2+u03V2uXh2Dqre9uQy3iddCA4NBTh0jGbGjQRCCC6preT3bV09OhgBoSZxzB0FcXqvTncC4K5tKyaFrsGbhajt8Gwizcq08pK13OSIH+5u5+VUlrgj2W7aXN0WZVnSfWz97V1xlqfda153WzbnVkVoMPSiLb4DrMuo58Vth/tj+fHHrIT/RZMknd5ntlk2/+pUMo5pKclI6HQcAkIQyDmefgEhIXhPLmTxjuqIa6OFD5ib8+gL64T3FpYE/XyzqZZTIiGODAW4rLaKjw5xCOdAeJ7uBKCi8iDaMy30zVkLoRP2vNxRp92yeTk35PHQEvWi90UT3B5NoqPCFIaAKxprWJXOki6wQQ7wt/YYhxck4panMtzjUscKqquuO0wx3Wew2qWpoXt8zk7LwnDp6jKEoNm0mR9QftSKdJZCVGuz5DP1VbyeManTNY6KBHtGjx8cCvCemgg3dSZ6/HEdJVnpE4Iv72yj03Fo0DXOqQyzIp3l9YxJhSY4tzLMcWM0hn60mOYzeE/tyGtAFOIZ3QmAP9BIbcMpxLuWY1kxfL46KmsOy5N/9Bh5liXT/LU91mNg/tuV4EN1lRyWM5iWlPy+tYvXcl6mDT0KMn9ujzLXZ7gmnrIondy+8d77YsmSirI6cHrOYJ1aEeLxRBqnTzuyX8B5uZK4JkN31cM1pcwbJe4D1xK57gGWpcrcTq0Is1/Az91dCXZZNgcFfcz1+/hLR2/DRKvt8PfOeE91RdqW3NClJlCcOMkN71jghRcmCIHAVOqbzmbK9HdT13j6XjMfbqJiSsl1uSkKVu7HBP7WEe8xavfGkqzJuIcDdpo2TSW6qDQoynpnnNLb8qPDvR52naHzjaYaDgn5qdU0Fgd8fLGhhnm52GKNrnNUOFDU9ntcJJinT3tYOFAUKvChEoL91XBbUvJgLMmKdJY9ts3TyQx3x4obJqC4cePuWLHojUcxntH1eFOyNWu5xi9F7j6ApxPpkuVdAmXo3L5ASqRbZ2PGZG06iyklJ/fTdVV4jqk+g0/UV3PV9Hq+0FhTNJXhA7WVvLMqQpOuUatpnBgOcnFBKVlE0/hsQzU1mkqeGcBBIT8XDSCheEdXgheSqhEkK5VoTjkt1qAaKP7Q1kX7OKt4TXS88ILHiOI4GeLR18hkdqBrYSJVBxAITB3vZRVRpWvYLht+W0qqch5jKY9EAw4LBajUdS6pqeBfnfHeqQsCjgoF+emeLuKOg0ANE/14fSVBVN1tXwzUFIXBYAPLUhm6HIktJU8m06zNmBwWDhDRNA4PBajUNRYG/PxkWh1ttkNYEz2x2/54skB6se9rLmfW88upLG9kOrlyWt2ELxUbLzxP12PEkNKmreVekonXsa0o2WwzHW2Pkk5tH++lFdFo6Mz3+fK8DgM1C6w7NnpiJOgqDrM44OOSWlVZcnxFiK821XBSJMgx4QCfqq9mUzZLu+2QkapyICUlV7dF+UR9dd75NNQooWMHqT3wRDzFZtMikxudk5Gw3bK5M5rkP11xvtbcxoZcWEQTgkZDL8vgAlguFyIBVGiCgFBqYv6e34ufL4G0dHqSkx7FeJ6ux4iRTm3NNXn08YmkTSz6MsHQzHFbVyk+3VDFjZ1xXsxJHR4RDnBxn+33GZVhdlk2LyQzGEJglxgYOcfv65lC0WU7NFvFsuICgYnkiqYa/hdN0mLZLAn4eGtVhNAgRVVeSmVKxli7Fdj+0h7lRzkhn8GwNBhgWSqTP3tEwOUN1XTYDrssm9k+g4V+gzVZi1+1dhUdw5LlaTW8WfGMrseIYVnRorE+ALZVYgz9OBPUNC6rq+KyEqqZek674B3VDh22zVTDGHCsTWnzKdGFYJ7fx6cbBqccV0hlGUa63XZIOJIKfXBG9+LaCnaYFntsG4GafnxBVYSZfh8zgb4qyvsH/czxGWwp6GTTBew7Ck0Fewue0fUYMXy+OoQwigyv4asZnwWNEFW61hPnHYhKXWOe32BD1sqLgeoIFg1zskU3Z1SGeS2T7XfqhAZDmnsW0TS+PaWWTVmLLsdhH7+v39d+SW0FP9vThS0lJqqTa2kwwPxRaJ/dW/DeGY8RIxCcgWHUYFoducnGAoRGVfXh4720MeXj9dX8vq2LbTk5yQpN41MDjCofDAsCPj5YW8m/uxJ02E5PFUbfut7jwsEhJ7KEEEUVE6WY4/fxw6l1PJtI0eVIDgz6WRzwTWppUVNKtmQtKjTB1FEY1+5NA/YYUaS0SSY2kElvRzciRCKLBi3EXorhTAMeD9osGzM3imY0jJCUSiIyZjv8qzPOqnQWvxCcFAlyfnUEfRIbvvFiRSrDX9rV6CcbyWyfwWcaqstORHbT3zRgz+h6TBomm9EdK7JS8nIqQ4flsG/Axz5+Y1J7muNFl+3wtea2vHFQBnBwyM/H6wfnOHgj2D089lLaLZv/19JJWjqYUomyLw0G+HBdpWd4B8nyVKaoYcYClqeyIzr+yqvT9fCYxNzcFSfqqJpgB9VF9ko6w+oS7csepSllUkf60uUZXQ+PHO2WzV3RBDd2xFmdVt7NeJJyHGID1LuuTptFNcEZqUTOPQbHIS4iQDqq+3Akdw1eeMHDA3gjY/LL1k4cqbaUTydTHBEKcmnd8DSNo7bDvzpjrExlMYTgxEiQC6oj/VYyJB2Hv7bHegznNJ/Ox+qqXDPpFZogZeebXR9QPYRysTc7VbrGx+qquDanPGdLyTy/wftGWO7RM7oeHsDf+0gXgvIWX0ilOTUbYtYga04dKXk5lWVFMs3KjElaShxUKdIjiRRJR/KBfoz5X9pjrE5ne7rCdpg2P93TyVXT6osqEs6uDHNTwew2XQiOjXgSi0PhoFCAX0z3s820qNC0PLnMkcIzuh5vekwp2e2ijCWlGiRZyuhaUvJ6xsSUkkUBH0FNQ0rJ71q7WJc1ybhEJ0wJzybTXFRT4dq8kHQcVvUxuKDqb7NSjWvfv2AW2vGRIBaSu6NJYo5krs/g/bWVZTdzeBRj5DoHR+34o3ZkD49JgoEasV44EVYXanS7GztNi5/t6ewpL3KQfLyuCp8QJQ1uX9JSUqx4q4xyqcBAxiXGLITglIowpwwwNHI4JByH5akMCdvhyHCQ2lHw/t5MeEbX402PEIK3Voa5K5bo2abrqE6yA12m7EopuaYtSqxAmPwP7VHOrAj3254LubbiEjHXal1taQsHRNo5b3qsWZXO8tvWrh7P+5ZokmNDAS6rH535YW8GvD2IhwdwZmWId1dX0KhrRDTBkeEAX2uqde3q6rAd2lzCERqCrJT4SyTJfKgW3Q8NUEP7sfoqKjRBXxNrA9e1x1xH9YwWlpRc3dZVJLL+TCrDiyWGb3oMjOfpenigvN2TKkKcVMaML58QJeed7RfwsSyVwbJlj7HyoaY27Bvwc0QoMGC8dYbP4IrGGr63u6PnNgdVBvbfrjgX1YzNlOgtWQurxAu9P5biiPDgdIA9FJ7R9fAYJJW6xr4BH+v6TO0VKC92SdDPN5pquT2aYGUqS6WucU5VmENLDIIsxQoXEXATeCaRGTOjG9ZKX1yKFYM9ysUzuh4eQ+Bj9VX8sS3K+lznV5Oh84n6KnQhqNSFmiwxjNmipaaMjaU0+DSfQZ2u0VbQoCGAk72StCHjGV0PjyEQ0TS+0FhDwnEwpaRGH9mM/uGhAPfEkvTtezBQ0y3Gkq811vDDlg46c0lDASwN+jl+kCOGPHrxjK6HxzAYrORfuUz1GVxcXcGNXXEMBDaSOT6DdxdM/R1tqg2dn05vYJdpsdO0mOX3lRw971EentH18JignFAR4vBwgM1ZixpdY9ooCGqXyzSfMebnd6TkiUSKpxIZdAGnVIQ4aoR1EMYDz+h6eExgQprGYpda4TcDf2uP8XK6dwjn9o4YO7IW76gZWS2Escar0/XwGEMyjmRtOsv2rDXuKmYTmTbLLpp6nJXwcDxF0pnck4Y9T9fDY4x4OZnmrx0xBAIHNcbn8oYaKj2dhCKaLRtDiKJmEF0I2m2H8CjF0seCybtyD49JRNR2uLYjRkYq3YWshJ2mzd87YuO9tAnJDJ/u2n1nI2kc4UqRscYzuh4eY8AKl1EwNrAyncX2wgxF1Og6J1UE8fd50/wC3lYVGdJo+YmEF17w8BgDNOGuHiYY+XEwewsXVVewMODnqUQaAzipIlQkbTkZ8Yyuh8cYcEgowI2d8bzbDOCQkB9tkpdAjRZCCA4NBQbdQj3R8cILHh5jQETT+HR9NRWaICCUgti+AZ9qF/Z4U+F5uh4eY8TioJ+fT6tnp2UTFoI6r7PrTYlndD08xhBNCGaOY2eZx/jj/fU9PN7kZKVkXcZEBxYGfK7C7R4jh2d0PTzexLyezvK7tihq/KXAJ+CLjTXM8LzxUcNLpHl4vEkxpeR3bVHSUpLONW3EHMnvW7u8FuVRxDO6Hh5vUroF2Avpchxa7cmtbzCR8Yyuh8ebFEMALmN3pOy+z2M08Iyuh8eblAV+H0Gh5XXEacAsv0HtJNc3mMh4RtfD402KJgRfbKxmqqHjQ2XV5/sNPlVfPd5L26vxUpQeHm9ipvoMvj+1jnbLRheCak9mctTxjK6Hh4fXHTeGeJc1Dw8PjzHEM7oeHh4eY4hndD08PDzGEM/oenh4eIwhntH18PDwGEOE9JqsPTw8PMYMz9P18PDwGEM8o+vh4eExhnhG18PDw2MM8Yyuh4eHxxjiGV0PDw+PMcQzuh4eHh5jyP8HygKhXsf3hc8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "\n",
    "model = RandomForestClassifier(n_estimators=100, random_state=0)\n",
    "visualize_classifier(model, X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that by averaging over 100 randomly perturbed models, we end up with an overall model that is much closer to our intuition about how the parameter space should be split."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Forest Regression\n",
    "\n",
    "In the previous section we considered random forests within the context of classification.\n",
    "Random forests can also be made to work in the case of regression (that is, with continuous rather than categorical variables). The estimator to use for this is the `RandomForestRegressor`, and the syntax is very similar to what we saw earlier.\n",
    "\n",
    "Consider the following data, drawn from the combination of a fast and slow oscillation (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(42)\n",
    "x = 10 * rng.rand(200)\n",
    "\n",
    "def model(x, sigma=0.3):\n",
    "    fast_oscillation = np.sin(5 * x)\n",
    "    slow_oscillation = np.sin(0.5 * x)\n",
    "    noise = sigma * rng.randn(len(x))\n",
    "\n",
    "    return slow_oscillation + fast_oscillation + noise\n",
    "\n",
    "y = model(x)\n",
    "plt.errorbar(x, y, 0.3, fmt='o');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the random forest regressor, we can find the best-fit curve as follows (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "forest = RandomForestRegressor(200)\n",
    "forest.fit(x[:, None], y)\n",
    "\n",
    "xfit = np.linspace(0, 10, 1000)\n",
    "yfit = forest.predict(xfit[:, None])\n",
    "ytrue = model(xfit, sigma=0)\n",
    "\n",
    "plt.errorbar(x, y, 0.3, fmt='o', alpha=0.5)\n",
    "plt.plot(xfit, yfit, '-r');\n",
    "plt.plot(xfit, ytrue, '-k', alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the true model is shown in the smooth gray curve, while the random forest model is shown by the jagged red curve.\n",
    "The nonparametric random forest model is flexible enough to fit the multiperiod data, without us needing to specifying a multi-period model!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Random Forest for Classifying Digits\n",
    "\n",
    "In Chapter 38 we worked through an example using the digits dataset included with Scikit-Learn.\n",
    "Let's use that again here to see how the random forest classifier can be applied in this context:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'frame', 'feature_names', 'target_names', 'images', 'DESCR'])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "digits = load_digits()\n",
    "digits.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To remind us what we're looking at, we'll visualize the first few data points (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x432 with 64 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up the figure\n",
    "fig = plt.figure(figsize=(6, 6))  # figure size in inches\n",
    "fig.subplots_adjust(left=0, right=1, bottom=0, top=1, hspace=0.05, wspace=0.05)\n",
    "\n",
    "# plot the digits: each image is 8x8 pixels\n",
    "for i in range(64):\n",
    "    ax = fig.add_subplot(8, 8, i + 1, xticks=[], yticks=[])\n",
    "    ax.imshow(digits.images[i], cmap=plt.cm.binary, interpolation='nearest')\n",
    "    \n",
    "    # label the image with the target value\n",
    "    ax.text(0, 7, str(digits.target[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can classify the digits using a random forest as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "Xtrain, Xtest, ytrain, ytest = train_test_split(digits.data, digits.target,\n",
    "                                                random_state=0)\n",
    "model = RandomForestClassifier(n_estimators=1000)\n",
    "model.fit(Xtrain, ytrain)\n",
    "ypred = model.predict(Xtest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the classification report for this classifier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       1.00      0.97      0.99        38\n",
      "           1       0.98      0.98      0.98        43\n",
      "           2       0.95      1.00      0.98        42\n",
      "           3       0.98      0.96      0.97        46\n",
      "           4       0.97      1.00      0.99        37\n",
      "           5       0.98      0.96      0.97        49\n",
      "           6       1.00      1.00      1.00        52\n",
      "           7       1.00      0.96      0.98        50\n",
      "           8       0.94      0.98      0.96        46\n",
      "           9       0.98      0.98      0.98        47\n",
      "\n",
      "    accuracy                           0.98       450\n",
      "   macro avg       0.98      0.98      0.98       450\n",
      "weighted avg       0.98      0.98      0.98       450\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn import metrics\n",
    "print(metrics.classification_report(ypred, ytest))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And for good measure, plot the confusion matrix (see the following figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "import seaborn as sns\n",
    "mat = confusion_matrix(ytest, ypred)\n",
    "sns.heatmap(mat.T, square=True, annot=True, fmt='d',\n",
    "            cbar=False, cmap='Blues')\n",
    "plt.xlabel('true label')\n",
    "plt.ylabel('predicted label');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that a simple, untuned random forest results in a quite accurate classification of the digits data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "This chapter provided a brief introduction to the concept of ensemble estimators, and in particular the random forest, an ensemble of randomized decision trees.\n",
    "Random forests are a powerful method with several advantages:\n",
    "\n",
    "- Both training and prediction are very fast, because of the simplicity of the underlying decision trees. In addition, both tasks can be straightforwardly parallelized, because the individual trees are entirely independent entities.\n",
    "- The multiple trees allow for a probabilistic classification: a majority vote among estimators gives an estimate of the probability (accessed in Scikit-Learn with the `predict_proba` method).\n",
    "- The nonparametric model is extremely flexible and can thus perform well on tasks that are underfit by other estimators.\n",
    "\n",
    "A primary disadvantage of random forests is that the results are not easily interpretable: that is, if you would like to draw conclusions about the *meaning* of the classification model, random forests may not be the best choice."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "jupytext": {
   "formats": "ipynb,md"
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
